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alexandr402 [8]
3 years ago
14

What is the solution to the system of equations? 5x-2y=-16 4x-5y=-23

Mathematics
1 answer:
Aleksandr [31]3 years ago
4 0

Answer:

The solution set is {-2, 3}.

Step-by-step explanation:

We can do this by elimination after manipulating the 2 equations so that the coefficients of  y  will disappear after addition:

5x - 2y = -16        Multiply this by -5:

-25x + 10y = 80 ...........(A)

4x - 5y = -23       Multiply this by 2:

8x - 10y = -46..............(B)

Now add A and B:

-17x = 34

x = 34/-17

<u>x = -2</u>.

Now substitute x = -2 into the first original equation:

5(-2) - 2y = -16

-2y = -16 +10 = -6

y = -6/-2

<u>y = 3</u>.

Confirm these results by substitution in the second original equation:

4(-2) - 5(3)

= - 8  - 15 = -23.

Checks OK.

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